We present a four-field virtual element discretization for the time-dependent resistive magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral meshes and guarantees velocity and magnetic fields that are divergence free up to machine precision. We provide a full convergence analysis under suitable regularity assumptions, which is validated by some numerical tests.
Beirao da Veiga, L., Dassi, F., Manzini, G., Mascotto, L. (2023). The virtual element method for the 3D resistive magnetohydrodynamic model. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 33(3), 643-686 [10.1142/S021820252350015X].
The virtual element method for the 3D resistive magnetohydrodynamic model
Beirao da Veiga, Lourenco;Dassi, Franco;Mascotto, Lorenzo
2023
Abstract
We present a four-field virtual element discretization for the time-dependent resistive magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral meshes and guarantees velocity and magnetic fields that are divergence free up to machine precision. We provide a full convergence analysis under suitable regularity assumptions, which is validated by some numerical tests.
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